(a) Field of the Invention
This invention relates to an apparatus methods of analyzing signals. The analyzed signals comprise of one or a finite number of simple vibratory (or sinusoidal) signals, in which an additive noise can be present. The first method is for measuring the signal constituents in terms of their respective frequencies, amplitudes and initial phases. The second method and an apparatus are for measuring the amount of shift between the corresponding constituents of two signals which have a common source, for example, measuring the time delay of a signal constituent received at two sensors. The third method and an apparatus are for detecting or selecting the dominant constituent of the analyzed signal.
There are many fields, (e.g. speech, seismic, radar and biomedical processing) in which a wide variety of vibratory signals are encountered, which can be represented by a summation of sinusoids or complex exponential functions. Some of these signals are characterized by a simple harmonic motion which can be approximately represented by a pure sinusoid, the vibration of a tuning fork is an example. Some signals have more complex periodic waveforms, which are formed by superpositions of some harmonically related simple harmonic motions which can be represented by summation of sinusoids with appropriate harmonically related frequencies, the voiced sound is a well known example. Many other signals comprise of superpositions of simple harmonic motions which are not harmonically related. These signals have irregular waveforms, however, they can still be represented by summation of the sinusoids, the vibrations resulted from operation of some mechanical systems have waveforms of this kind. Additive noise is usually an element of these signals.
Frequently, it is desirable to be able to analyze these signals, whether it is periodic or not, and to break them down into components or extract essential parameters which can be readily handled for collecting or conveying information. It offers the advantage of signal reduction which leads to saving in signal storage or signal transmission. The analysis results can also provide great insight into the characteristics of an unknown physical phenomena from which the signal is produced. It is known that any signal can be built up from a set of pure sinusoids or complex exponential functions of appropriate frequencies, amplitudes and initial phases. By superposition of the resultant series of sinusoids, or complex exponential functions, one can resynthesize or recreate the original waveform.
(b) Description of the Prior Art
With the advent of digital signal processing, many proposals have been made for analyzing complex signals by spectral analysis methods. This approach has been proved to be essential for advanced communication, control and signal interpretation systems. Known methods can be categorized as parametric or non-parametric. Conventional methods are based on the Fourier Transform, and are non-parametric. Most modern methods assume a rational transfer function model, ARMA (Auto-Regressive, Moving-Average), and hence they are parametric, such methods achieve high frequency resolution, at the expense of enormous computations. These techniques are described in "Spectrum Analysis--A Modern Perspective" by S. K. Kay, and S. L. Marple Junior, in the proceedings of the IEEE, volume 69, No. 11, November, 1981, pages 1380-1419, and in "Digital Signal Processing" edited by N. B. Jones, IEE Control Engineering Series 22, 1982. Known techniques cannot be simultaneously both fast and accurate.
The conventional Fourier Transform approach is based on a Fourier series model of the signal. It enables the real-time production of the power spectral density for a large class of signals. Many spectrum analyzers are based on this technique. In general, such a technique is fast and relatively easy to implement, and works well for very long sampled signal and when the signal-to-noise ratio is low. However, this approach has the disadvantage that it lacks adequate frequency precision for small number of samples. The frequency precision in Hertz is approximately equal to a discrete frequency in size, which is the reciprocal of the observatioin interval. This becomes more of a problem when the signal has time-varying spectrum, as for example in the case of speech. Likewise the frequency resolution in multi-dimensional analysis is inversely proportional to the extent of the signal. Alos, one has the problem of spectral leakage, due to the implicit windowing of the singal resulting from the finite number of samples. This distorts the spectrum, and can further reduce the frequency precision. Therefore, it is not a good method for neasuring frequencies of major constituents in the signal. Since this is a non-parametric approach, both the magnitude and the phase spectrum are required to unambiguously represent a signal in the time domain. Hence, it is not used for signal storage or transmission. Traditionally, the phase spectrum of the Fourier Transform has been ignored. It has generally been believed that the magnitude spectrum is more important than the phase spectrum, because the magnitude spectrum shows explicitly the signal,s frequency content. Indeed, in some techniques, the initial phase information has been lost.
Modern spectral estimation methods, developed in the past two decades, are based on a time series model ARMA, mentioned above. Such methods can have the advantage of providing higher frequency resolution. However, it should be noted that such higher frequency resolution can be achieved only under large signal to noise ratios. When this ratio is low, these methods do not give better frequency resolution than the classical Fourier Transform method. The computational requirements of these methods are much higher, and this makes them unattractive, and possibly impractical, for real-time processing.